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Abstract

NS Contact We studied the linear response of a normal metal superconducting metal contact to a small electric field. In a preparatory section the order-parameter profile and the density of states were calculated in equilibrium. We showed that the density of states in the normal metal is unaltered if the impurity self-energies are not taken into account while the coherence in the superconductor is always affected by the presence of the normal metal. Self-consistent calculations result in an impurity-induced proximity effect in the normal metal. This proximity effect causes a spatially constant gap in the density of states of the normal metal if the normal metal is sandwiched between two superconductors. The dynamics of the NS contact is strongly dominated by the conservation law for charge and local charge neutrality which together fully determine the current in one-dimensional systems. For answering the question how this constant current is established in the non-homogeneous NS contact, the quasiclassical equations were solved including the self-consistencies for the order parameter, the impurity self-energies, and the electrochemical potential. The latter was used to deduce an internal electric field as response to the external perturbation. The internal field is of same order as the perturbation and is caused by charges which are either bound to the interface or spread over several coherence lengths. The surface charges are not due to the step in the order parameter at the interface but solely to abrupt changes of the impurity scattering. The order parameter itself can only produce continuous charge densities. The charges are indirectly calculated using Maxwell's equations. They are of higher order in the expansion parameters of Fermi-liquid theory and are hence beyond this theory. Nevertheless, their effect has to be considered to be consistent in leading order. Weak links in He3 We investigated several methods of calculating the current-phase relation of weak links in He3. In the limit of small holes the hole itself and the current through it does not affect the order parameter in the superfluid and the current can hence be calculated using the pinhole model. This leads to a periodic current-phase relation. It was shown that the pair-breaking effect of the separating wall has no significant influence on the functional dependence of the current on the phase difference. The wall mainly reduces the amplitude of the current. For orifices with radii comparable with the coherence length, self-consistent order-parameter fields were calculated. The two fixed phases of the pinhole model are then replaced by a field which allows the phase to wind up continuously. This not only breaks the periodicity, but also leads to multivalued current-phase relations. Over a wide range the current through the orifice is linear in the phase difference between the reservoirs. Although this is expected in the hydrodynamic limit, the hydrodynamic equations are not applicable as they always fail at the edges of the circular apertures. However, calculating the current quasiclassically with the phase determined via the Laplace equation gives a fairly good approximation to the fully self-consistent solution. This approximation becomes weak for larger phase differences when pair-breaking due to the current itself has to be taken into account. Remarkably, the maximal current through the aperture is sandwiched between the pinhole current and the depairing current for a homogeneous superfluid which differ only by a factor of about two at low temperature in spite of the drastic difference of the models. A quasiclassical free-energy functional was introduced and it was stressed that this choice is not unique and that a whole zoo of different functionals exists. The functional was used to investigate the change in free energy due to the wall, the orifice, and the phase difference.